Enterprise Risk Management Formula Book

Appendix A.6: Probability Distributions: Distributional families

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Exponential family


A (continuous) random variable  (multivariate or univariate) follows a distribution from the exponential family, with vector parameter , if its probability (density) function can be written in the form:



or equivalently as:



The  are automatically determined once the other functions have been chosen because .  is called the natural parameter.


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